There are two main tests in use.Reverse-transcription polymerase and Serology testing.
"The Center of Disease Control (CDC) has developed a real-time reverse-transcription polymerase chain reaction for diagnostic purposes."
"Serology testing, leverages ELISA antibody test kits to detect the presence of antibodies produced by the host immune system against the virus. The CDC runs two ELISA tests against two different proteins produced by the virus."
"Since antibodies continue to circulate even after the infection is cleared, serology tests continue to be positive for individuals who have been previously exposed and developed an immune response, which means a positive test may not indicate an active infection."
For the true geeks on GC including OMG
The Stanford test uses a technique called reverse-transcriptase polymerase chain reaction, or RT-PCR, to rapidly identify the presence of viral RNA in swabs from the noses of potentially infected people. RT-PCR uses short stretches of DNA called primers that bind tightly and specifically only to matching sequences in SARS-CoV-2 RNA. An enzyme called reverse transcriptase then converts the viral RNA into complementary DNA, and as the reaction continues, an enzyme called polymerase is used to generate billions of DNA copies that can be detected by fluorescently tagged molecules called probes.